Dividing Fractions: Word Problems

Apply your fraction division skills to solve real-world problems!

1. Single-Step Word Problems

Key Problem Types

Sharing: "Total is shared so each gets X. How many people?"

Cutting: "Total is cut into pieces of size X. How many pieces?"

Filling: "Total poured into containers of size X. How many containers?"

Example 1: Juice Bottles

There are $1\frac{3}{4}$ litres of juice in Jug A and $2\frac{1}{4}$ litres of juice in Jug B.

(a) How many litres of juice are there in both jugs altogether?

(b) John has some empty bottles. The capacity of each bottle is $\frac{4}{5}$ litre. He pours all the juice from both jugs into the bottles, filling each bottle completely. How many bottles does he fill?

ShowHide solution

Part (a): Total juice

$1\frac{3}{4} + 2\frac{1}{4} = 3\frac{4}{4} = 4$ litres

There are 4 litres of juice altogether.

Part (b): Number of bottles

Remember the Rule:

Dividing by

\frac{4}{5}

is the same as multiplying by

\frac{5}{4}

4 ÷

\frac{4}{5}

= 4 ×

\frac{5}{4}

Working:

4 ÷

\frac{4}{5}

= 4 ×

\frac{5}{4}

\frac{4 × 5}{1 × 4}

\frac{20}{4}

= 5 (simplified)

Answer:5

John fills 5 bottles.

Example 2: Puzzle Completion

Ramli took $\frac{1}{12}$ h to complete a puzzle. How many such puzzles did he complete in $\frac{3}{4}$ h?

ShowHide solution

Remember the Rule:

Dividing by

\frac{1}{12}

is the same as multiplying by 12

\frac{3}{4}

\frac{1}{12}

\frac{3}{4}

× 12

Working:

\frac{3}{4}

\frac{1}{12}

\frac{3}{4}

× 12

\frac{3 × 12}{4 × 1}

\frac{36}{4}

= 9 (simplified)

Answer:9

Ramli completed 9 puzzles.

2. Multi-Step Word Problems

Problem-Solving Strategy

Draw a bar model to visualise the problem
Identify what's given and what you need to find
Work step by step, solving one part at a time
Check if your answer makes sense

Example 3: Sharing Pizza

Julie, Tom and Ben had a pizza. Julie ate $\frac{1}{4}$ of the pizza. Tom and Ben shared the rest of the pizza equally.

(a) What fraction of the pizza did Tom and Ben share?

(b) What fraction of the pizza did Tom have?

Pizza Problem

The pizza is divided into 4 equal parts

ShowHide solution

Part (a): Tom and Ben's share

Pizza Problem

The pizza is divided into 4 equal parts

Remainder = $1 - \frac{1}{4} = \frac{3}{4}$

Tom and Ben shared $\frac{3}{4}$ of the pizza.

Part (b): Tom's fraction

Remember the Rule:

Dividing by 2 is the same as multiplying by

\frac{1}{2}

\frac{3}{4}

÷ 2 =

\frac{3}{4}

\frac{1}{2}

Working:

\frac{3}{4}

÷ 2

\frac{3}{4}

\frac{1}{2}

\frac{3 × 1}{4 × 2}

\frac{3}{8}

Answer:

\frac{3}{8}

Tom had $\frac{3}{8}$ of the pizza.

Example 4: Peter's Money

Peter spent $\frac{2}{5}$ of his money on a pair of pants and $\frac{2}{3}$ of the remainder on 6 identical T-shirts. What fraction of the money did Peter spend on each T-shirt?

Peter's Money

Peter's money divided into 5 equal parts

ShowHide solution

Step 1: Find the remainder

Remainder after pants = $1 - \frac{2}{5} = \frac{3}{5}$

Step 2: Find fraction spent on T-shirts

Fraction on T-shirts = $\frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}$

Peter's Money

Peter's money divided into 5 equal parts

Step 3: Find fraction per T-shirt

Remember the Rule:

Dividing by 6 is the same as multiplying by

\frac{1}{6}

\frac{2}{5}

÷ 6 =

\frac{2}{5}

\frac{1}{6}

Working:

\frac{2}{5}

÷ 6

\frac{2}{5}

\frac{1}{6}

\frac{2 × 1}{5 × 6}

\frac{2}{30}

\frac{1}{15}

(simplified)

Answer:

\frac{1}{15}

Peter spent $\frac{1}{15}$ of his money on each T-shirt.

3. Challenging Problems

Example 5: Paper Clips

There are some blue paper clips and green paper clips in a container. $\frac{2}{3}$ of the paper clips are blue and the rest are green.

The blue and green paper clips are packed separately into boxes. Sam packs the blue paper clips. Each of his boxes holds $\frac{1}{12}$ of all the paper clips in the container. Mei packs the green paper clips. Each of her boxes holds $\frac{1}{9}$ of all the paper clips in the container. How many boxes do they need to pack all the paper clips?

ShowHide solution

Step 1: Find boxes for blue clips

Remember the Rule:

Dividing by

\frac{1}{12}

is the same as multiplying by 12

\frac{2}{3}

\frac{1}{12}

\frac{2}{3}

× 12

Working:

\frac{2}{3}

\frac{1}{12}

\frac{2}{3}

× 12

\frac{2 × 12}{3 × 1}

\frac{24}{3}

= 8 (simplified)

Answer:8

8 boxes are needed for the blue paper clips.

Step 2: Find fraction of green clips

Green clips = $1 - \frac{2}{3} = \frac{1}{3}$

Step 3: Find boxes for green clips

Remember the Rule:

Dividing by

\frac{1}{9}

is the same as multiplying by 9

\frac{1}{3}

\frac{1}{9}

\frac{1}{3}

× 9

Working:

\frac{1}{3}

\frac{1}{9}

\frac{1}{3}

× 9

\frac{1 × 9}{3 × 1}

\frac{9}{3}

= 3 (simplified)

Answer:3

3 boxes are needed for the green paper clips.

Final Answer:

Total boxes = 8 + 3 = 11 boxes

Problem-Solving Tips

When to Use Division

"How many groups/pieces/people?"
"Shared equally... how many?"
"Cut into pieces of size X"
"Each container holds X"

Common Mistakes to Avoid

Forgetting to find the remainder first
Dividing in the wrong order
Not simplifying the final answer
Forgetting units in the answer

Key Takeaways

Draw a bar model to visualise multi-step problems

Find the remainder first when something is "used" or "spent"

Work step by step - don't try to do everything at once

Check your answer - does it make sense in the context?

Include units in your final answer (litres, kg, pieces, etc.)